Abstract

This paper examines the interplay of the effect of cross immunity and antibody-dependent enhancement (ADE) in multistrain diseases. Motivated by dengue fever, we study a model for the spreading of epidemics in a population with multistrain interactions mediated by both partial temporary cross immunity and ADE. Although ADE models have previously been observed to cause chaotic outbreaks, we show analytically that weak cross immunity has a stabilizing effect on the system. That is, the onset of disease fluctuations requires a larger value of ADE with small cross immunity than without. However, strong cross immunity is shown numerically to cause oscillations and chaotic outbreaks even for low values of ADE.

Received 23 July 2009Accepted 10 November 2009Published online 04 December 2009

Lead Paragraph: The spreading of infectious diseases having multiple strains in a population can exhibit very complex dynamics, ranging from periodic and quasiperiodic outbreaks to high-dimensional chaotic behavior. Several sociological and epidemiological factors characterize the disease spread at different levels, such as interactions among the disease strains, social contacts, and human immune responses. In this work we focus on dengue fever, a vector borne disease which has exhibited as many as four different strains, and is endemic in large areas of Southeast Asia, Africa, and the Americas. A notable feature of dengue is its interaction with the human immune system. When an individual is infected with dengue, the immune system triggers an antibody response which will temporarily protect against secondary infections. However, when the level of protection decreases, secondary infections may be possible and the presence of low level antibodies triggers an increase in the infectiousness of the individual. This effect is called antibody-dependent enhancement (ADE). In this paper we study a mathematical model for the spreading of dengue fever. While ADE alone is proved to trigger large amplitude chaotic oscillations, we show that including weak temporary cross immunity stabilizes the system. In contrast, we also show that strong cross immunity destabilizes the dynamics. These results will help understand the implementation of proper control strategies when using future vaccines.

Acknowledgments:

L.B.S. and S.B. were partially supported by the Jeffress Memorial Trust. I.B.S. was supported by the Office of Naval Research and the Armed Forces Medical Intelligence Center. The authors acknowledge helpful discussions with Derek Cummings.